scripts/TP1 04.12 Harmonic Oscillator.LACE

   1 # Harmonic Oscillator
   2 # A mass m is subject to a force F=-k*r.
   3 # What is the trajectory if the mass starts at position (a,0,0)?
   4 # How much time does it take to pass through zero?
   5 # What is the trajectory if it starts at (a,0,0) with velocity (0,v0,0)?
   6 # Compare to the case including gravity on earth in x direction
   7 # m*x'' = -k*x +        g
   8 # m*y'' = -k*y (z can be set to 0).
   9
  10 coefficient.1(-1) -> -a    # (a,0,0), has to be negative because x' is negative
  11 coefficient.2     -> k/m_x # k/m for x
  12 coefficient.3(+1) -> v0    # (0,v0,0), has to be positive because y'' is positive
  13 coefficient.4     -> k/m_y # k/m for y, identical to k/m for x
  14 coefficient.5(-1) -> -g     # g
  15
  16 iintegrate x'' -> -x'
  17 iintegrate -x' -> x
  18    IC: -a
  19 cmultiply (k/m_x, x) -> k/m*x
  20 isum (k/m*x, -g) -> -k/m*x+g
  21 assign (-k/m*x+g) -> x''
  22
  23 iintegrate y'' -> -y'
  24    IC: v0
  25 iintegrate -y' -> y
  26 cmultiply (k/m_y, y) -> k/m*y
  27 invert (k/m*y) -> -k/m*y
  28 assign (-k/m*y) -> y''
  29
  30 output x -> out.x
  31 output.y -> out.y